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# If the standard deviation of Set Y is 4, what is the range

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If the standard deviation of Set Y is 4, what is the range [#permalink]  14 Jul 2009, 18:48
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67% (01:09) correct 33% (00:40) wrong based on 12 sessions
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If the standard deviation of Set Y is 4, what is the range of scores that fall within one standard deviation?

(1) The median of Set Y is 5.

(2) The mean of Set Y is 6.
[Reveal] Spoiler: OA
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Re: Standard Deviation [#permalink]  14 Jul 2009, 23:55
Ans "B"
Range = Mean +/- std deviation
So st 2 provides the info on mean of set. and can be answered.
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Re: Standard Deviation [#permalink]  15 Jul 2009, 19:58
I agree with you. But my concern is that we dont need either of the statements to come to the conclusion that range is 8. We are given that std dev is 4 in the question. So obviosuly the first standard dev has scores that fall within a range of 8. So we dont either of the stmts to answrt the question....

Example we are told mean is 6. So first std dev has scores ranging from 2 (6-4) to 10 (6+4).
Example 2. Lets say we are told mean is 20. So first std dev has scores ranging from 16 (20-4) to 24 (20+4)

In either case, the range is always going to be 8.Am I correct? Can somebody explain why we need statement B?
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Re: Standard Deviation [#permalink]  16 Jul 2009, 05:06
Expert's post
The answer is E; neither statement is at all helpful. Taking the question literally, we need to find the range (i.e. largest - smallest) of the set of values which are greater than M -4 and less than M + 4, where M is the mean. It's clear that the range is no larger than 8, but you can't assume that the range is in fact 8. Take, for example, the following data set:

$$\{ -2\sqrt{10}, 0, 0, 0, 2\sqrt{10} \}$$

The standard deviation of this set is 4, and the set of values within one standard deviation of the mean is simply {0,0,0}, which has a range of 0.

I'd guess the question designer intended to ask something different with this question. If the 'correct' answer is B, I'd guess that the question designer meant 'range' in the colloquial sense (the question might be trying to say: values within one s.d. of the mean must lie between which min and max values?), and not the sense in which the word is used on the GMAT or in real statistics (largest-smallest). If that's the intended meaning, it's a badly written question, and you would never encounter such ambiguity on the real test. What is the source?
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Re: Standard Deviation [#permalink]  16 Jul 2009, 06:54
I remember solving this in OG and yes i did the same mistake and gave it a B but the answer is 'E'.

As soon as I saw the question I knew it right off the bat..

My answer is B but OG ans is E

But IanStewart your explanation is good it makes sense. By knowing SD, mean you cant determine the range .
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Re: Standard Deviation [#permalink]  16 Jul 2009, 09:07
Expert's post
This is definitely not a question from the OG. The question asks about the 'range of scores' without mentioning that the set contains 'scores'. It also asks for the range that 'fall within one standard deviation'. Within one standard deviation of what? No official question would ever have such wording.
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Re: Standard Deviation [#permalink]  19 Jul 2009, 17:51
Ian, I found this question in MGMAT forums, where it was mentioned that it is from one of their CAT exams.
Re: Standard Deviation   [#permalink] 19 Jul 2009, 17:51
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